The SI unit and dimensions of Stefan’s constant σ in case of Stefan’s law of radiation is

Question

The SI unit and dimensions of Stefan’s constant σ in case of Stefan’s law of radiation is (A) (J/m3 s4), [M1L0T-3K-4] (B) (J/m2 s4 K), [M1L0T-3K3] (C) (J/m3s K4), [M1L0T-3K4] (D) (J/m2s K4), [M1L0T-3K-4]

Tardigrade Admin · Accepted Answer

According to Stefan's law, energy emitted by a body per unit area per second is proportional to fourth power of the absolute temperature.

E = σ T^{4}

where,

E =

energy emitted/area/second,

T =

absolute temperature in kelvin
and

σ =

Stefan's constant.

\Rightarrow σ = \frac{E}{T ^{4}}

Unit of Stefan's constant

\Rightarrow \frac{J / m ^{2} s}{K ^{4}} = J / m^{2} s K^{4}

Dimensions of Stefan's constant,

σ = \frac{[ Energy ]}{[Area] \times [ Time ] \times [ Temperature ] ^{4}}

= \frac{[ M L ^{2} T ^{- 2} ]}{[ L ^{2} T \times K ^{4} ]} = [M^{1} L^{0} T^{- 3} K^{- 4}]

Q. The $S I$ unit and dimensions of Stefan’s constant $σ$ in case of Stefan’s law of radiation is

$\frac{J}{m ^{3} s ^{4}}, [M^{1} L^{0} T^{- 3} K^{- 4}]$

$\frac{J}{m ^{2} s ^{4} K}, [M^{1} L^{0} T^{- 3} K^{3}]$

$\frac{J}{m ^{3} s K ^{4}}, [M^{1} L^{0} T^{- 3} K^{4}]$

$\frac{J}{m ^{2} s K ^{4}}, [M^{1} L^{0} T^{- 3} K^{- 4}]$

Q. The SI unit and dimensions of Stefan’s constant σ in case of Stefan’s law of radiation is

m3s4J​,[M1L0T−3K−4]

m2s4KJ​,[M1L0T−3K3]

m3sK4J​,[M1L0T−3K4]

m2sK4J​,[M1L0T−3K−4]

Q. The $S I$ unit and dimensions of Stefan’s constant $σ$ in case of Stefan’s law of radiation is

$\frac{J}{m ^{3} s ^{4}}, [M^{1} L^{0} T^{- 3} K^{- 4}]$

$\frac{J}{m ^{2} s ^{4} K}, [M^{1} L^{0} T^{- 3} K^{3}]$

$\frac{J}{m ^{3} s K ^{4}}, [M^{1} L^{0} T^{- 3} K^{4}]$

$\frac{J}{m ^{2} s K ^{4}}, [M^{1} L^{0} T^{- 3} K^{- 4}]$